If your grown up children had an unfavorable opinion on a new partner of yours, yet you have no issues with the new partner yourself, would you listen to them?
Or is it really none of their business?

It depends on what their grievances are. But I doubt my kids would soon do such a thing, like I don't do it to them. They want me to be happy and feel it's not their business.
If they had good reason to have their doubts I'd actually like to hear it though so I have another perspective and don't get blindsided.

Your kids could have past experiences that would create a false representation of who your new partner is.
best thing to do is to continue as normal with your new partner, and if your children show signs of being emotional (anger, sadness etc) then be there silently until the emotions pass. try not to make a big deal out of it as all emotions pass and the thoughts that are associated with the emotions will pass with them.
resist their emotions and you'll be only helping them hold onto them by suppressing them.
hope this helps

I think people we are close to, family and friends, see things that we may
not see, or want to see, in our partner. Love can be blind. Honestly, I’ve
never taken their advice, but they always ended up being right. There’s
a lesson in that.

My policy is to listen to any and all advice, but weigh it and test it myself, so that whatever I do, will be because I myself think it's the best way to go.

Oh, and one sort of side issue that often seems to come up in such situations: if anyone involved declares that what I decide will be a test of my loyalty to them, I will shut them down immediately. Perhaps not shut them out of my life, but make it clear to them that I don't tolerate making love dependent on manipulative obedience like that.

Whilst i feel, that a relationship is pretty much
an "A & B conversation, and that others should
C their way out.

I don't see where a grown child having an
opinion, harms anything. Unless,, of course,
the grown child is trying to sway the opinion
of others.

After living alone for so long my kids are happy I now have someone in my life that makes me smile.

I would listen but if it was just an opinion with no other grounds I would not change anything